Solve (1/2+1/3)-(2/3-1/3-frac{1}{6})

$$( \frac { 1 } { 2 } + \frac { 1 } { 3 } ) - ( \frac { 2 } { 3 } - \frac { 1 } { 3 } - \frac { 1 } { 6 } )$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{3}{6}+\frac{2}{6}-\left(\frac{2}{3}-\frac{1}{3}-\frac{1}{6}\right)$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+2}{6}-\left(\frac{2}{3}-\frac{1}{3}-\frac{1}{6}\right)$$

Add 3 and 2 to get 5.

$$\frac{5}{6}-\left(\frac{2}{3}-\frac{1}{3}-\frac{1}{6}\right)$$

Since \frac{2}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}-\left(\frac{2-1}{3}-\frac{1}{6}\right)$$

Subtract 1 from 2 to get 1.

$$\frac{5}{6}-\left(\frac{1}{3}-\frac{1}{6}\right)$$

Least common multiple of 3 and 6 is 6. Convert \frac{1}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{5}{6}-\left(\frac{2}{6}-\frac{1}{6}\right)$$

Since \frac{2}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}-\frac{2-1}{6}$$

Subtract 1 from 2 to get 1.

$$\frac{5}{6}-\frac{1}{6}$$

Since \frac{5}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-1}{6}$$

Subtract 1 from 5 to get 4.

$$\frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$